# Vortrag

Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

## Fourier coefficients of continuous measures on the Furstenberg sequence

Vortrag von Prof. Dr. Sophie Grivaux

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 14.10.19  Zeit: 14.00 - 15.00  Raum: ETH HG G 43

We will present a negative answer to a conjecture of Lyons, related to Furstenberg $x2$-$x3$ conjecture, concerning the existence of a continuous probability measure on the unit circle with large Fourier coefficients on the Furstenberg set {2^p3^q ; p,q \geq 0}. The proof involves rigidity sequences for weakly mixing dynamical systems, and a generalization of a recent construction of such sequences by Fayad and Thouvenot. This is joint work with Catalin Badea.